Simulations and observables in relativistic cosmology

Abstract

The huge leap in volume and precision that will be achieved by upcoming large sky surveys will make our observables sensitive to a number of effects previously ignored, such as relativistic effects. These can potentially represent new systematics to take into account, but also new probes for our cosmological models.

In this thesis, we explore novel tools to model these type of effects, with a particular emphasis on frame-dragging --- the leading order post-Newtonian effect --- in cosmological -body simulations.

In the first part, we discuss the implementation of a new code for general-relativistic simulations in cosmology, . The code is built upon the numerical infrastructure of the code, and implements a constrained formulation of general relativity in which scalar and vector modes of the spacetime metric are calculated fully nonlinearly. We perform several tests against both theory and well-established, state-of-the-art relativistic codes, demonstrating that is able to produce robust results. Furthermore, we introduce a new, general method to generate initial conditions for particles, which circumvents the gauge issues affecting the standard prescriptions.

In the second part, we focus on exploring the impact of frame-dragging on different scenarios. Firstly, based on a high-resolution run with , we explore the behaviour of this effect in different types of dark matter haloes. In particular, we show that, although the gravitomagnetic force acting on dark matter is small relative to the Newtonian force, it can be up to one order of magnitude larger than previous literature results.

Finally, we explore the possibility of detecting the gravitomagnetic effect that appears in lensing convergence maps via cross-correlations with the kinetic Sunyaev-Zel'dovich effect, which is imprinted in maps. We make forecasts for next-generation weak-lensing surveys such as and , and experiments such as Simons Observatory and , and find that the gravitomagnetic effect can be detected on small angular scales, provided that several foreground contaminations can be reliably removed.